A bullet is fired horizontally at a speed of 200 m/s at a target 100m away. calculate:1)how far the bullet will have fallen when it hits the target.

2)the angle it then makes the horizontal

To find the distance the bullet will have fallen when it hits the target, you can use the equations of motion.

1) The horizontal velocity of the bullet remains constant, so we can assume there is no acceleration in the horizontal direction. The equation for horizontal motion is:

Distance = Velocity x Time

We are given the velocity of the bullet (200 m/s) and the distance it travels horizontally (100 m). Rearranging the equation, we have:

Time = Distance / Velocity

Time = 100 m / 200 m/s
Time = 0.5 s

Now, we need to calculate the vertical distance the bullet has fallen during this time. In the vertical motion, we have acceleration due to gravity. The equation for vertical motion is:

Distance = Initial velocity x Time + (1/2) x Acceleration x Time^2

Since the bullet is fired horizontally, the initial vertical velocity is 0 m/s. The acceleration due to gravity is approximately 9.8 m/s^2. Plugging in these values, we get:

Distance = 0.5 x 9.8 x (0.5)^2
Distance = 0.5 x 9.8 x 0.25
Distance = 1.225 m

Therefore, the bullet would have fallen approximately 1.225 meters when it hits the target.

2) To find the angle the bullet makes with the horizontal after hitting the target, we can use trigonometry. The tangent of an angle is equal to the vertical distance divided by the horizontal distance.

tan(angle) = Vertical distance / Horizontal distance

tan(angle) = 1.225 m / 100 m

Taking the inverse tangent of both sides, we find:

angle = arctan(1.225 m / 100 m)

Using a calculator, we find:

angle ≈ 0.012 radians

To convert this to degrees, multiply by 180/π:

angle ≈ 0.012 radians x (180/π)
angle ≈ 0.69 degrees

Therefore, the angle the bullet makes with the horizontal after hitting the target is approximately 0.69 degrees.

1) 1.68